Summer 2020 undergraduate research programs - SPUR and REU

You are here

Summer 2020 Department of Mathematics Undergraduate Research Programs

SPUR PROGRAM - Summer Program for Undergraduate Research
REU PROGRAM - Research Experience for Undergraduates

SPUR Program Projects 1 & 2

Project 1 of the SPUR Program has been cancelled for Summer 2020

**Due to COVID-19 and the University moving to online instruction for classes and programs starting before July 12th, Projects 2 and 3 will be conducted remotely for the 8 weeks of research.  We are in the process of working out logistical details and will post more information here soon.


Directed Robert S. Strichartz

Please refer to the “**PLEASE NOTE:” statement under “Other Details” section below regarding earlier arrival for this project.

Students in this project will study properties of functions defined on fractals. For certain fractals, including the Sierpinski gasket, the Sierpinski carpet, and some of the classical Julia sets, there is now a theory of “differential equations.” (See my book, Differential Equations on Fractals, a tutorial, Princeton University Press, 2006.) One of the goals of this project is to obtain more information about solutions of these fractal differential equations, following up on work that has been done by past REU students. Most of the work on this project will involve both computer experimentation and theoretical study, but individual students may put more emphasis on one or the other. We expect that students will be involved in all stages of the process: planning what examples to study, doing the programming for the computations, and interpreting the results (and attempting to prove the conjectures that come out of the process).


Directed by Andy Borum

This project will focus on analyzing deformable structures that can alter their shape in response to changes in their environment.  The structures we will consider come from applications in medicine, manufacturing, and robotics.  We will first analyze the mechanical properties of these structures using tools from optimization and dynamical systems theory.  Then we will develop methods for how the structures should alter their shape to achieve a desired goal while also avoiding undesirable phenomena such as buckling and snapping instabilities.

Students participating in this project should have strong backgrounds in linear algebra, ordinary differential equations, and have some previous experience with computer programming.  Additional experience with optimization, mechanics, or control theory will be helpful, but is not required.  The problems in this project will involve both computational and analytical methods.

REU Program Project 3


Directed by Alex Townsend-Math and Alex Townsend-CAM

Please refer to the “**PLEASE NOTE:” statement under “Other Details” section below regarding earlier arrival for this project.

This project will focus on the analysis, implementation, and derivation of numerical solutions for the solution of partial differential equations on triangulated geometries. Within numerical methods for solving differential equations, we will be exploring numerical methods based on orthogonal polynomials, domain decomposition methods, and spectral methods. We hope to build a range of computational tools to extend and generalize existing numerical tools for solving high-frequency wave propagation problems and resonance calculations. 

Students participating in this project should have strong backgrounds in linear algebra and ordinary differential equations.  Previous experience with computer programming and computational mathematics will be very helpful. The problems will involve computational and analytical skills. 


WHEN:  Both the REU and SPUR Programs are 8 week programs that run from June 15, 2020 – August 7, 2020

**PLEASE NOTE - **Due to concerns and evolving changes in response to COVID-19, both the Fractals Conference and CAM Workshop have been cancelled (4/8/2020):  Students accepted into Project 1 with Robert Strichartz and Project 3 with Alex Townsend are required to arrive 1 week earlier to attend the Fractals Conference for project 1 students, and the CAM Modeling Workshop ( hosted by the Department of Center for Applied Mathematics in conjunction with the Department of Mathematics for project 3 students.  The CAM project is still in the beginning stages of planning.  Information and details will be posted once it comes available.

WHERE: Mathematics Department, Malott Hall, Cornell University, Ithaca, NY 14853-4201.

These summer programs provide the opportunity for undergraduate students of mathematics to participate in leading-edge research.  This year, some projects are designated "SPUR" and others are designated "REU."  The difference between SPUR and REU projects is the funding support that is available.


Any student funding that is provided for the SPUR program comes from the Cornell Department of Mathematics.  To receive Cornell funding you must be a Cornell student, but do not need to be a US citizen or resident.  Cornell students may apply for departmental support of $3,500.00.  Non-Cornell students are welcome to apply and participate in the program, but there is no funding available. 

The REU project is supported by the NSF ( RTG Grant, so students who are U.S. citizens or permanent residents are eligible to apply, and if selected will receive funding support of $5,000.00 under this NSF grant.

We welcome applications from all students including Cornell, non-Cornell, and international students (see below under International Students).  Those who apply to the programs as self-funded applicants will still be subject to the same competitive selection process.

Participants will arrange for their own housing.  The Math Department will assist with providing information on housing and contact information to make reservations. 

After you are selected you are registered as a Cornell Student as follows:

  1. If you are accepted to either program and you are a student (US or non-US/International) currently attending and enrolled at a U.S. academic institution and in a full-time 4-year undergraduate program you will be registered through Cornell Summer Session, and a registration fee to the student does not apply.
  2. International students are registered through the Summer Session under the umbrella of the PIRIP Program (Provost’s International Research Internship Program):  We welcome international students to apply!  The PIRIP Program does NOT apply to international students who are currently full-time students enrolled in a 4 year undergraduate program at a U.S. academic institution (as stated in the paragraph above).  The PIRIP Program only applies to full-time international students who are currently attending non-US institutions and are coming directly from their international institution OR who are international students currently at a U.S. institution enrolled in an exchange or internship program.  International students accepted to the REU or SPUR programs will be self-funded and will be registered through Cornell Summer Session under the umbrella of the PIRIP Program.  The student is responsible for paying an administrative fee of $2,280.00 for summer 2020, which is a scholarship that is 25% of the current summer extramural tuition rate for 6 credits.  Ex.) Summer 2020 fee = $1,520.00 tuition per credit x 25% x 6 credits = equals an administrative fee of $2,280.00.  In addition, you will also be required to carry adequate health insurance that is in compliance with Cornell health insurance requirements.  If you do not have a current plan you can purchase one on your own, which Cornell will review and approve for compliance.  Cornell also offers a Student Health Insurance Plan (SHIP) that you can purchase, which is already in compliance.  The program SHIP cost for Summer 2020 is approximately $775.00.  You will also earn 6 credits - Satisfactory or Unsatisfactory (not a letter grade).

CU PIRIP Student total expenses will include:

  • Administrative fee = $2,280.00 – Applies to students in number 2 listed above.
  • Health Insurance = $775.00 estimated (if you are arriving earlier for project 1 or project 3) – Applies to students in number 2 listed above that are not in compliance with CU insurance requirements.
  • Housing/living costs (applies to all REU/SPUR students) – housing can range from approximately $60.00 - $125.00/week depending single/double occupancy and where you stay.  Generally students stay in Coop Housing on campus, which is most affordable.  Plus food and other living expenses.

To apply you will need the following:

  1. Statement about your background, educational goals, and your scientific interests.  Include whatever further information you consider relevant and be sure to include information about your computer experience.
  2. At least two letters of recommendation, which can be uploaded to the application portal.  The reference writer is notified to upload their letter once you enter their information on the application.
  3. Transcripts (unofficial transcripts are accepted), which can be uploaded to the application portal.


Please go to REU/SPUR Application to apply.  The deadline to submit your application is February 27, 2020 and offers will be made on approximately March 3, 2020.  If you have comments, questions, or concerns please send e-mail to the SPUR and REU coordinators at


Cornell University is committed to providing a safe, inclusive, and respectful learning, living, and working environment. To this end, Cornell will not tolerate sexual and related misconduct. Through Cornell University Policy 6.4, and the applicable procedures, the university provides means to address bias, discrimination, harassment, and sexual and related misconduct, including gender-based harassment, sexual harassment, sexual assault, domestic and dating violence, stalking, and sexual exploitation. Reports of bias, discrimination, and harassment can be made online at or by contacting the Office of the University Title IX Coordinator at